On the Finitary Characterization of-Congruences (original) (raw)
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2019
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A Few Remarks on Congruent Numbers
Rocky Mountain Journal of Mathematics, 2009
... TERUTAKE ABE, ASHVIN RAJAN AND FRANC OIS RAMAROSON Dedicated to Professor Takashi Ono ... is a triangle whose three sides all have rational lengths.) We call ( 2)-congruent numbers "congruent numbers." Our inspiration was the following pretty density argument ...
Remarks on special congruences
2022
We study algebras and varieties where every non-trivial congruence has some class being a non-trivial subuniverse of the algebra in question. Then we focus on algebras where this non-trivial class is a unique non-singleton class of the congruence. In particular, we investigate Rees algebras, quasi-Rees algebras and algebras having the one-block-property. We also present results concerning these properties on quotient algebras. Several examples of such algebras and varieties are included.
Some modifications of the congruence extension property
Mathematica Slovaca, 1995
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A characterization of identities implying congruence modularity / by Alan Day and Ralph Freese
0. Introduction. In his thesis and [24], J. B. Nation showed the existence of certain lattice identities, strictly weaker than the modular law, such that if all the congruence lattices of a variety of algebras J^ satisfy one of these identities, then all the congruence lattices were even modular. Moreover Freese and Jônsson showed in [10] that from this "congruence modularity" of a variety of algebras one can even deduce the (stronger) Arguesian identity.
A characterization of identities implying congruence modularity. I
Canadian Journal of Mathematics, 1980
0. Introduction. In his thesis and [24], J. B. Nation showed the existence of certain lattice identities, strictly weaker than the modular law, such that if all the congruence lattices of a variety of algebras J^ satisfy one of these identities, then all the congruence lattices were even modular. Moreover Freese and Jônsson showed in [10] that from this "congruence modularity" of a variety of algebras one can even deduce the (stronger) Arguesian identity.